# Projectile motion in a spring loaded gun

## Homework Statement

1. A Turbo Booster toy that launches a 60-gram “insect” glider projectile by compressing a helical spring and then releasing the spring when the trigger is pulled. When pointed upward the glider should ascend approximately 8 m before falling. The launcher is made with carbon steel wire, with a diameter of d=1.1 mm. The coil diameter is D=10 mm. Calculate the number of turns N in the spring such that it would provide the necessary energy to the glider. The total working deflection is x=150 mm with a clash allowance of 10%.

## Homework Equations

I need to used conservation of energy to find initial velocity and spring constant I believe. Final velocity is 0. Not sure how to find the number of turns in the spring though.

KE=1/2*m*V^2
PE=m*g*h

## The Attempt at a Solution

g=9.81 m/s^2 gravity
d=1.1 mm wire diameter
D=10 mm col diameter
m=60 gm mass of toy
x=150 mm working deflection
dist= 8 m distance traveled

C=D/d=10/1.1= 9.091 spring index
G=11.2*10^6 psi (for carbon steel)
k=?
V=?

somehow need number of turns

Last edited:

## Answers and Replies

trying to bump this up

Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
This looks like it's outside the scope of a standard introductory physics class, which normally does not discuss how the number of turns and wire diameter related to the spring constant.

I am wondering if your professor has given you additional material on this?

At any rate, it is possible to find the spring constant k using conservation of energy methods.

minger
Science Advisor
This is definately a combination of physics and mechanical design. You have the correct approach. Conservation of energy will allow you to calculate the spring constant needed to impart the correct amount of energy needed to reach 8 m. From here, you can use the equation for the spring constant of a helical spring (as obtained from Shigley's Chapter 10-3)
$$k = \frac{d^4 G}{8D^3 N}$$
Where d is the wire diameter, D is the mean spring diameter, G is the shear modulus of the material, and N is the....tada, number of turns in the spring.

Good luck,

p.s. tex is still down, so try to read this for the spring constant
k = (d^4 * G) / (8D^3 N)